Actuality, necessity, and logical truth

Philosophical Studies 130 (3):437 - 459 (2006)
Abstract
The traditional view that all logical truths are metaphysically necessary has come under attack in recent years. The contrary claim is prominent in David Kaplan’s work on demonstratives, and Edward Zalta has argued that logical truths that are not necessary appear in modal languages supplemented only with some device for making reference to the actual world (and thus independently of whether demonstratives like ‘I’, ‘here’, and ‘now’ are present). If this latter claim can be sustained, it strikes close to the heart of the traditional view. I begin this paper by discussing and refuting Zalta’s argument in the context of a language for propositional modal logic with an actuality connective (section 1). This involves showing that his argument in favor of real world validity his preferred explication of logical truth, is fallacious. Next (section 2) I argue for an alternative explication of logical truth called general validity. Since the rule of necessitation preserves general validity, the argument of section 2 provides a reason for affirming the traditional view. Finally (section 3) I show that the intuitive idea behind the discredited notion of real world validity finds legitimate expression in an object language connective for deep necessity.
Keywords actuality  contingent a priori  deep necessity  general validity  logical truth  necessary a posteriori  real world validity  superficial necessity
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    Lloyd Humberstone (2011). Variation on a Trivialist Argument of Paul Kabay. Journal of Logic, Language and Information 20 (1):115-132.

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